Theoretically you can sell anything although I do think the market for used mattresses is limited unless you find a friend or family member - realistically would you want to buy a mattress from a stranger?
When I was in college, people bought mattresses from Goodwill (they were fumigated) but now charities won't take them but you might contact a shelter for abused women because perhaps they take them since they are always in dire need of household items.
You can do a search of craigslist in your area and see what people are asking for them.
Some days I pray for Silence, Some days I pray for Soul,
Some days I just pray to the God of Sex and Drums and Rock 'N' Roll.